Primary normal stress coefficient shear rate dependence

Fig. 7.15. PE under steady state shear flow at 150 °C Strain rate dependencies of the viscosity ry, the primary normal stress coefficient and the recoverable shear strain 7e. The dotted line represents Eq. (7.122). Results obtained by Laun [76]...

From Eq. 83 we observe that the viscometric functions are insensitive to the direction of shear and that the primary normal stress coefficient is zero. Hence this is not a realistic model for most shear sensitive fluids. Eq. 82, with i = fi = constant and / 2 = 0 is the Newtonian fluid. If we keep ii shear rate dependent and set /t,2 = 0, we then have the GNF. Several special cases of the GNF are discussed below. 

It should be noted that as t becomes large the lowest order term in the coefficient of the K-term is just 60, that is one half the zero-shear-rate value of the primary normal stress function. A similar result was obtained by Bird and Marsh (7) and by Carreau (14) from the slowly varying flow expansions of two continuum models. Hence the time-dependent behavior of the shear stress is related to the steady-state primary normal stress difference in the limit of vanishingly small shear rate. 

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